Kepler's third law states that the square of the orbital period of a planet is proportional to

Question

BlackTom AI · Accepted Answer

Kepler's third law relates the time a planet takes to orbit to the size of its orbit. 
Option 1: 'its orbital semimajor axis cubed.' This matches the classic formulation P^2 ∝ a^3, where P is the orbital period and a is the semimajor axis, so this statement is correct. 
Option 2: 'the reciprocal of its orbital semimajor axis.' This would imply P^2 ∝ 1/a, which is not how Kepler's law is defined; the relationship increases with a, not decreases, so this is incorrect. 
Option 3: 'its mass squared.' Kepler's third law does not state any dependence on the planet's mass for the orbital period in the two-body approximation; in fact, for planets around the Sun, the mass is negligible in comparison to the Sun, so this option is false. 
Option 4: 'its orbital semimajor axis.' While a appears in the law, the equation involves a cubed, not simply a, so stating a alone does not capture the correct proportionality; this is incomplete and thus incorrect. 
Option 5: 'its density squared.' Density has no role in Kepler's third law about orbital periods, so this is incorrect. 
In summary, only the first option expresses the correct proportional relationship between P^2 and a^3 as stated by Kepler's third law.

ASTRON 2140 AU2025 (23428) Quiz 1 - 2025 Sep 19

Kepler's third law states that the square of the orbital period of a planet is proportional to

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